This paper deals with the problem of shipping multiple commodities from a single vendor to a single buyer. Each commodity is assumed to be constantly consumed at the buyer, and periodically replenished from the vendor. Furthermore, these replenishments are restricted to happen at discrete time instants, e.g., a certain time of the day or a certain day of the week. At any such time instant, transportation cost depends on the shipment quantity according to certain discount scheme. Specifically, we consider two transportation quantity discount schemes: LTL (less-than-truckload) incremental discount and TL (truckload) discount. For each case, we develop MIP (mixed integer programming) mathematical model whose objective is to make an integrated replenishment and transportation decision such that the total system cost is minimized. We also derive optimal solution properties and give numerical studies to investigate the problem. / Singapore-MIT Alliance (SMA)

I tillverkande företag kan inköpskostnaden stå för 60–80 procent av den totalaproduktkostnaden. Det framhäver vikten av att identifiera en kostnadseffektiv inköpsstrategi som reducerar totalkostnad för inköp. En sådan inköpsstrategi kan vara inköp av större ordervolym för att erhålla volymbaserat pris. Tidigare forskning om volymbaserat pris centreras kring inköp av standardkomponenter i stora volymer, således finns en bristande forskning om volymbaserat pris för organisationer som inte tillämpar denna typ av inköp. Studien syftar därför till att med en explorativ fallstudie, studera hur ökad ordervolym med samkoordinerade inköp påverkar totalkostnad för inköp hos en organisation med hög kundanpassning och låg årlig ordervolym. En organisation som arbetar enligt engineer-to-order (ETO) med storskaliga projekt, hög kundanpassning och låg årlig ordervolym har således använts som huvudsaklig empirisk kontext för fallstudien. Datainsamlingen har i fallstudien bestått av en metodkombination som inkluderar en dominerande kvalitativ fas följt av en underliggande kvantitativ fas. Insamlade data användes sedan i en kostnadsanalys för att utvärdera hur identifierade faktorer påverkade organisationens totalkostnad för inköp och huruvida samkoordinerade inköp kan anses som en kostnadseffektiv inköpsstrategi i denna kontext. Resultatet från studien visar att inköpspris reduceras och lagerkostnad ökar vid samkoordinerade inköp för organisationer med hög kundanpassning och låg årlig ordervolym. Den köpande organisationen kan påverka faktorerna: ordervolym och utformning av artiklar, vilket skapar en kostnadsförändring för leverantörernas faktorer: tillverkning, material, transport och administration. Kostnadsanalysen visar att kostnadsreducering uppnås vid samkoordinerade inköp för den studerade organisationen. Viss osäkerhet kring resultatet uppstår då samkoordinerade inköp skapar en ny situation för lagerhantering där kostnadsuppgifter saknas. Enligt studien kan synergierna av samkoordinerade inköp förstärkas genom ett skifte mot single sourcing, centraliserade inköp och ökad grad av standardisering. Studiens främsta bidrag är en identifikation av de faktorer som påverkas i leverantörernas verksamhet vid en kombination av samkoordinerade inköp och karaktäristiken av ETO, samt hur dessa genererar volymbaserat pris. / In manufacturing companies, the purchase cost can account for 60-80 percent of the total product cost. The high purchase cost emphasizes the importance of identifying a cost-effective purchasing strategy that reduces the total cost of purchasing. Such a purchasing strategy can be to purchase larger order volumes in order to obtain quantity discounts. Previous research on quantity discounts is centered on the purchase of standard components in large volumes, thus a lack of research on quantity discounts for organizations that do not apply this type of purchase exists. Therefore, this study aims to examine how a larger order volume with coordinated purchases affects the total cost of purchasing for an organization with high customer customization and low annual order volume. It was done with an exploratory case study of an organization that operates according to engineer-to-order (ETO) with large-scale projects, high customer customization and low annual order volume. The data collection in the case study consisted of a mixed-method approach that includes a dominant qualitative phase followed by an underlying quantitative phase. The collected data was further used in a cost analysis to evaluate how identified factors affected the organisation's total cost of purchasing and whether coordinated purchases can be considered a cost-effective purchasing strategy in this context. The result of the study shows that the purchase price is reduced, and the inventory cost is increased by coordinated purchases for organizations with high customer customization and low annual order volume. The purchasing organization can affect the factors: order volume and design of items, which results in a cost change for the supplier’s factors: manufacturing, materials, transport and administration. The cost analysis shows that a cost reduction is achieved through coordinated purchases for the studied organisation. Some uncertainties about the result arises as coordinated purchases create a new situation for inventory management where cost data is missing. The synergies of coordinated purchasing can further be enhanced by a shift towards single sourcing, centralized purchasing and increased degree of standardization. The main contribution of the study is the identification of factors in the suppliers' operations that are affected by the combination of coordinated purchases and the characteristics of ETO, and how they generate quantity discounts.

This thesis considers two kinds of problems, motivated by practical applications in data center operations and maintenance. Data centers are the brain of the internet, each hosting as many as tens of thousands of IT devices, making them a considerable global energy consumption contributor (more than 1 percent of global power consumption). There is a large body of work at different layers aimed at reducing the total power consumption for data centers. One of the key places to save power is addressing the thermal heterogeneity in data centers by thermal-aware workload distribution. The corresponding optimization problem is challenging due to its combinatorial nature and the computational complexity of thermal models. In this thesis, a holistic theoretical approach is proposed for thermal-aware workload distribution which uses linearization to make the problem model-independent and easier to study. Two general optimization problems are defined. In the first problem, several cooling parameters and heat recirculation effects are considered, where two red-line temperatures are defined for idle and fully utilized servers to allow the cooling effort to be reduced. The resulting problem is a mixed integer linear programming problem which is solved approximately using a proposed heuristic. Numerical results confirm that the proposed approach outperforms commonly considered baseline algorithms and commercial solvers (MATLAB) and can reduce the power consumption by more than 10 percent. In the next problem, additional operational costs related to reliability of the servers are considered. The resulting problem is solved by a generalization of the proposed heuristics integrated with a Model Predictive Control (MPC) approach, where demand predictions are available. Finally, in the second type of problems, we address a problem in inventory management related to data center maintenance, where we develop an efficient dynamic programming algorithm to solve a lot-sizing problem. The algorithm is based on a key structural property that may be of more general interest, that of a just-in-time ordering policy. / Thesis / Doctor of Philosophy (PhD) / Data centers, each hosting as many as tens of thousands of IT devices, contribute to a considerable portion of energy usage worldwide (more than 1 percent of global power consumption). They also encounter other operational costs mostly related to reliability of devices and maintenance. One of the key places to reduce energy consumption is through addressing the thermal heterogeneity in data centers by thermal-aware work load distribution for the servers. This prevents hot spot generation and addresses the trade-off between IT and cooling power consumption, the two main power consump tion contributors. The corresponding optimization problem is challenging due to its combinatorial nature and the complexity of thermal models. In this thesis, we present a holistic approach for thermal-aware workload distribution in data centers, using lin earization to make the problem model-independent and simpler to study. Two quite general nonlinear optimization problems are defined. The results confirm that the proposed approach completed by a proposed heuristic solves the problems efficiently and with high precision. Finally, we address a problem in inventory management related to data center maintenance, where we develop an efficient algorithm to solve a lot-sizing problem that has a goal of reducing data center operational costs.